RECTANGULAR BEAMS 129 



use of a smaller percentage of steel, and the cost is still further 

 reduced. Thus it should be clear that the proportions of a beam 

 will not be determined by shear excepting as to minimum cross- 

 section an increase in depth always resulting in a gain in 

 economy. It should be noted in this connection, however, that 

 although deep beams are economical of concrete, the wooden 

 forms cost more than they do for shallow beams. 



63. Restrained Beams. The discussion thus far in the course 

 has related mainly to rectangular reinforced concrete beams, 

 reinforced for tension and shear, and simply supported. It must 

 be known by the student, however, that the ends of a reinforced 

 concrete beam are often fixed, as in all-concrete construction. 

 Such beams sometimes span only one opening, but more often 

 they are continuous over several supports. It is sometimes 

 difficult to provide a sufficient amount of restraint at the ends 

 of such beams to be able to consider the ends entirely fixed, and 

 good judgment should be used in the design for all such cases. 

 Restrained beams of one span only will be considered under this 

 heading, leaving the treatment of continuous beams, both fixed 

 and supported ends, for a later discussion. 



A smaller beam may be used .when the beam is considered 

 restrained than when considered simply supported, so that a 

 beam computed as simply supported is always on the safe side. 

 For example, the moment at the center of a restrained beam 

 of one span, with both ends fixed, due to a uniform load over the 

 entire beam, is 1/24 wl 2 , where w is the load per linear foot of 

 beam (maximum shear 0.5 wl). Also, a restrained beam with one 

 end fixed and the other free, and under the same conditions 

 as above, has a moment of 9/128 wl 2 (maximum shear 5/8 wl). 

 A simply supported beam, on the other hand, has the much 

 greater moment at the center of 1/8 wl 2 . 



Before one can appreciate the design of beams in all-concrete 

 construction, it will be necessary to have a clear understanding 

 of what is meant by a restrained beam, and the amount of re- 

 straint which is necessary to make the beam fixed. A restrained 

 beam may be defined as a beam fastened at one or both ends in 

 such a manner that the beam is not free to deflect at these 

 points. A beam cannot be considered entirely fixed at either 

 point, however, unless the restraint is sufficient to cause the 

 neutral surface at that point to be horizontal. 



An example of a beam completely fixed at the ends is shown 



